Thermodynamic modelling of a recompression CO2 power cycle for low temperature waste heat recovery

Applied Thermal Engineering 107 (2016) 441–452

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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng

Research Paper

Thermodynamic modelling of a recompression CO2 power cycle for low temperature waste heat recovery Shubham Banik a,⇑, Satyaki Ray b, Sudipta De c a

Department of Mechanical Engineering, McMaster University, 1280 Main St W, Hamilton, ON L8S 4L8, Canada Department of Mechanical Engineering, IIT Madras, Sardar Patel Rd, Adyar, Chennai, Tamil Nadu 600036, India c Department of Mechanical Engineering, Jadavpur University, 188 Raja S.C. Mullick Road, Kolkata 700032, India b

h i g h l i g h t s

g r a p h i c a l a b s t r a c t


Thermodynamic model for

recompression T-CO2 is developed.
Energetic and exergetic analysis

compared with S-CO2 and Reg. Brayton cycle.
Maximum efficiency of 13.6% is obtained for T-CO2 cycle.
Optimum recompression ratio of 0.48 is obtained for minimum irreversibility.
Reg. Brayton has better efficiency, TCO2 offers minimum irreversibility.

a r t i c l e

i n f o

Article history: Received 4 February 2016 Revised 24 June 2016 Accepted 29 June 2016 Available online 30 June 2016 Keywords: CO2 power cycle Transcritical cycle Recompression Efficiency Irreversibility

a b s t r a c t Due to the rising prices of conventional fossil fuels, increasing the overall thermal efficiency of a power plant is essential. One way of doing this is waste heat recovery. This recovery is most difficult for low temperature waste heat, below 240 °C, which also covers majority of the waste heat source. Carbon dioxide, with its low critical temperature and pressure, offers an advantage over ozone-depleting refrigerants used in Organic Rankine Cycles (ORCs) and hence is most suitable for the purpose. This paper introduces parametric optimization of a transcritical carbon dioxide (T-CO2) power cycle which recompresses part of the total mass flow of working fluid before entering the precooler, thereby showing potential for higher cycle efficiency. Thermodynamic model for a recompression T-CO2 power cycle has been developed with waste heat source of 2000 kW and at a temperature of 200 °C. Results obtained from this model are analysed to estimate effects on energetic and exergetic performances of the power cycle with varying pressure and mass recompression ratio. Higher pressure ratio always improves thermodynamic performance of the cycle – both energetic and exergetic. Higher recompression ratio also increases exergetic efficiency of the cycle. However, it increases energy efficiency, only if precooler inlet temperature remains constant. Maximum thermal efficiency of the T-CO2 cycle with a recompression ratio of 0.26 has been found to be 13.6%. To minimize total irreversibility of the cycle, an optimum ratio of 0.48 was found to be suitable. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction

⇑ Corresponding author. E-mail address: [email protected] (S. Banik). http://dx.doi.org/10.1016/j.applthermaleng.2016.06.179 1359-4311/Ó 2016 Elsevier Ltd. All rights reserved.

Global energy demand increases with increasing population and living standard. Electricity is the most convenient form of secondary energy. Presently, coal-based power plants are major

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Nomenclature A CFC cp cv E h H HTR I LH LTR _ m ORC OD p Q_ r rp R s S-CO2 T-CO2 T TIP TIT U

v

_ W

recuperator area (m2) Chlorofluorocarbon isobaric specific heat (kJ/kg K) isochoric specific heat (kJ/kg K) exergy (J) specific enthalpy (kJ/kg K) heat source high temperature recuperator irreversibility (kJ) both low and high temperature low temperature recuperator mass flow rate (kg/s) Organic Rankine Cycle ozone depletion pressure (kPa) rate of heat (kW) recompression mass ratio pressure ratio Universal gas constant specific entropy (kJ/kg K) supercritical CO2 transcritical CO2 temperature (K) Turbine Inlet Pressure (kPa) Turbine Inlet Temperature (°C) overall heat transfer coefficient (kW/m2 K) specific volume (m3/kg) power (kW)

source of electricity worldwide [1]. Unfortunately, these power plants together are the largest emitter of CO2 as a single sector and its availability is rapidly decreasing [2], inflicting major climate changes [3]. For better sustainability in energy, enhanced energy efficiency is a critical requirement. Industrial waste heat is a large source of energy that can be recovered for improving energy efficiency. According to the US Department of Energy [4], as much as 20–50% of the energy consumed is ultimately lost via waste heat contained in streams of hot exhaust gases and liquids. Grade of waste heat is determined by its temperature and is usually divided into three categories – high grade (>650 °C), medium grade (240–650 °C) and low grade (<240 °C). Low grade waste heat accounts for more than 50% of all the waste heat generated by the industry [5]. Low grade waste heat is also most difficult to recover and it may not be economically using conventional technologies. Conversion of waste heat to power is the best possible utilisation thermodynamically. This is possible even for low grade heat if gases with low critical temperatures are used as working fluid for power generation, but it requires adequate parameters for selection and equipment design [6]. Organic Rankine Cycles (ORCs) have been frequently used as bottoming cycles for power generation process [7] from waste heat. These cycles use organic substances (such as ammonia, R11, R12, R113, R123, R134a) [8]. The constant temperature heat exchange process in ORCs creates the problem of ‘‘pinching” which limits the performance of heat exchangers. Also many working fluids contain ozone-depleting Chloro-fluoro Carbons (CFCs), and hence pose a threat to the environment. Non-toxic environment friendly CO2 cycles are thus preferred over conventional ORCs. CO2 as working fluid has certain advantages over the ORCs [9]. Carbon dioxide easily attains super-critical state. Pressure and temperature of CO2 at critical point are 7.38 MPa and 31.1 °C respectively. It is a non-toxic and non-corrosive substance. It has

WHRU

Waste Heat Recovery Unit

Greek alphabets isentropic efficiency thermal efficiency second law efficiency recuperator effectiveness

g gth gII e

Subscripts a ambient c compressor CH contact heater pc pre-cooler f flue gas gen generation H heat source 1, 2, 3 state points in input is isentropic L low temperature out outlet p pump rev reversible t turbine th thermal 0 dead state I first law II second law

zero ozone depletion potential [10]. This may also indirectly contribute towards reducing global CO2 emissions using waste heat as an energy source and thus increasing energy efficiency. CO2 cycles can constitute a supercritical cycle where the whole cycle lies above the critical point or transcritical cycle where the cycle remains partly above and partly below critical point, or it may be simple Brayton cycle. Carbon dioxide has also been used as a working fluid in bottoming cycles in offshore oil and gas installations [11]. Supercritical carbon dioxide (S-CO2) has been used for ‘‘remanufacturing cleaning” [12] in contrast to thermal cleaning for oil residues in several engines. In the past S-CO2 power cycle has been studied using solar energy [13,14] and even with a heat source at a temperature as low as 200 °C [15]. A small scale model was built that showed feasibility and achieved efficiencies between 8.8 and 9.5% [16]. Transcritical carbon dioxide (T-CO2) power cycle is a cycle where a part of the cycle (heat addition) remains in the supercritical zone whereas the heat rejection part lies below the critical conditions. T-CO2 power cycle has certain thermodynamic benefits over the traditional ORCs. The supercritical heat addition process of the cycle offers better temperature glide during heat exchange process [17]. Hence, the problem of pinching reduces, decreasing the irreversibility. This cycle can be used for low temperature automotive exhausts to drive subsidiary appliances [18] as well as refrigeration cycles [19]. T-CO2 power cycle has also been used for power generation from waste heat [20] using low temperature heat sources [21] along with the optimization of the ‘‘UA” product (the ‘effective’ heat exchanger area) [22]. A modelling study for comparison of T-CO2 cycle with ORCs using R123, R245fa, R600a and R601 [23] for low temperature geothermal heat sources shows a 10.9% efficiency for T-CO2 cycle as compared to a maximum of 14.05% for that of R601 at a turbine inlet pressure of 14.4 MPa. Feher ensured the presence of liquid at the precooler exit of a

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S. Banik et al. / Applied Thermal Engineering 107 (2016) 441–452

condenser and regenerator) value when used with a regenerator as compared to ones without it. A T-CO2 cycle without regenerator has minimum optima for both ‘‘UA” and total area, which explains that the higher ‘‘UA” value governed by the regenerator cannot be nullified by that of the vapour generator reduction. In this work, a detailed thermodynamic model is developed for a T-CO2 power cycle with recompression. Performance of this cycle is estimated both on the basis of energy and exergy analyses. Results are obtained from the developed model with specific assumptions. Effects of variation of pressure ratio as well as recompression mass ratio on thermodynamic performance of the power cycle are discussed. Results are explained relating to practical aspects involving cycle efficiency and irreversibilities. Comparison of the performance of T-CO2 power cycle with that of supercritical and regenerative Brayton cycles for comparable operating parameters are also presented.

transcritical cycle and thereby used a pump for minimal work input [24]. According to a comparative study carried out by Chen et al. [17], the power output of the T-CO2 power cycle was slightly higher than the ORC using R123 as working fluid. A major drawback of a simple transcritical cycle, as pointed out by Kim et al. [25], is the huge cycle irreversibility. Feher [24] mentions that the problem is due to the internal irreversibility of the recuperator which occurs both in T-CO2 and S-CO2 cycles. Sarkar and Bhattacharyya [26] performed an optimization of a recompression S-CO2 cycle with reheat. Kim et al. [25] further elaborated the fact that in case of low temperature operations, preferably below 150 °C, there was a significant difference in values of isobaric specific heats (cp) of CO2 at high and low pressure sides. Recompression or partial condensation cycles [27] were introduced to address this problem. For recompression, recuperator is divided into two sections high and low temperature ones. Recompression cycle uses a trans-critical or super-critical cycle, where a part of the fluid stream from the low temperature recuperator in the lowpressure side is recompressed to the high pressure side without entering the precooler. The recompressed fluid stream joins the main stream before the high temperature recuperator and hence recuperators have unequal mass flow rates. Since, the mass of the fluid is sufficiently reduced in the high pressure side before recombination, the difference in cp values between the two pressure zones is compensated and the temperature of the recuperator exit stream after being heated is higher than earlier. Usage of two recuperators for high and low temperatures was suggested by Wang et al. [28]. For practical installation of the entire system, the total conductance (‘‘UA” product) [29] plays an important part and influences the economics. Analysis of a T-CO2 power cycle with low temperature heat source made by Cayer et al. [22] points out a significantly high total ‘‘UA” (sum of the product of the overall heat transfer coefficient by the area, W/K for vapour generator,

2. Description of the power cycle

Compressor

The schematic of the T-CO2 power cycle is shown in Fig. 1 and the corresponding T-s diagrams for transcritical and supercritical cycles are given in Figs. 2 and 3 respectively. Similar configurations can be used for the S-CO2 and Brayton cycle as well. As shown in Fig. 1, CO2 is compressed from state 1 to 2 in a pump (for transcritical cycle) or a compressor (for supercritical or Brayton cycle). Pressure ratio across the pump/compressor is assumed to be the same across the power turbine as any pressure drop due to fluid flow is neglected. At the inlet to the pump, CO2 is in liquid state for T-CO2 cycle. However, for S-CO2 cycle it is in gaseous state and hence a compressor must be used. Compressed CO2 passes through two closed heat exchangers – a low temperature recuperator (LTR) and a high temperature recuperator (HTR) through state points 2–3 and 4a–5 respectively. In between these two, there is another contact heater for transcritical and supercritical CO2 power cycles. This contact heater is not used in regenerative Brayton cycle. In LTR

Pump / compressor

Q in

Waste Heat Recovery Unit

6

Gas Turbine

1

5

4

2

7 3

Contact heater

4a

Pre-cooler

Q out

8

9 Low Temperature Recuperator

High Temperature Recuperator

Fig. 1. Layout of T-CO2/S-CO2 recompression cycle.

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S. Banik et al. / Applied Thermal Engineering 107 (2016) 441–452 Table 1 Process description with all state points.

6

T

Q in

4s

4a

4

7 7s

8

3 2s

Process

1–2 2–3 3/4–4a

Sub cooled CO2 pumped to high pressure High pressure CO2 stream heated in LTR Recompressed fluid stream mixed with high pressure stream at contact heater High pressure CO2 stream heated in HTR CO2 stream heated by waste heat source in WHRU High pressure CO2 stream expansion in the turbine Low pressure CO2 stream releases heat in HTR Low pressure CO2 stream releases heat in LTR Part of low pressure CO2 stream recompressed to high pressure Heat rejected in the pre-cooler/condenser

4a–5 5–6 6–7 7–8 8–9 9–4 9–1

5

2

State points

9

1 Q out

Table 2 Assumptions made for simulating the cycle. 1. 2. 3. 4.

s Fig. 2. T-s diagram of the T-CO2 cycle with recompression.

6

T

Q in

4s

4a

8

depending on the type of cycle. As an option, a part of the total CO2 mass is compressed in a compressor (called recompression) and the remaining CO2 passes through the pre-cooler (called partial condensation). State points as indicated in the schematic (in Fig. 1) are also shown in corresponding T-s diagrams (Figs. 2 and 3). The state points and their respective processes have been described in Table 1. 3. Modelling of power cycles

9

2s

1

7

7s

5

3 2

4

Extraneous heat loss was neglected Losses due to fluid flow were neglected Isentropic efficiency (gt) of turbine was assumed to be 90% Isentropic efficiencies of compressor (gc) and pump (gp) were both assumed to be 85% 5. Ambient conditions were assumed to be 1 bar, 300 K 6. Waste heat was taken as 200 °C (Tf) 7. State of CO2 at the exit of precooler was saturated liquid for the T-CO2 8. Maximum cycle temperature (T6) was assumed as 443 K 9. Kinetic and potential energies of fluid streams were neglected 10. Effectiveness (e) of the recuperator was taken as 0.85

Q out

s Fig. 3. T-s diagram of the S-CO2 cycle with recompression.

and HTR, recuperative heat exchange occurs between high pressure and low pressure CO2 as shown in Fig. 1. For recompression (or partial condensation) a part of total mass flow of CO2 from state point 9 is compressed in a compressor to state 4 and then mixed with the high pressure CO2 stream (state point 3) between LTR and HTR for transcritical and supercritical cycles at state 4a. Heated CO2 from these heat exchangers (state 5) is then passed through the Waste Heat Recovery Unit (WHRU) where low temperature heat (at 200 °C) is added to it. CO2 gas from WHRU exit (state 6) expands in a gas turbine delivering power. Exhaust low pressure CO2 from the gas turbine at state 7 passes through HTR (state point 8) and LTR (state point 9) in its return path to exchange heat with high pressure CO2 stream. Pre-cooler subsequently cools the low temperature CO2 before it goes to the pump/compressor at state 1. Heat exchange in the precooler may be two phase (for transcritical cycle) or single phase (for supercritical or Brayton cycles),

The T-CO2 power cycle is suitable for low temperature heat source. Industrial low temperature waste heat used for this cycle was assumed to be at a rate of 2000 kW and at a temperature of 200 °C. This means the inlet at WHRU shown in Fig. 1 is at 200 °C. The simulations were carried out in MATLAB 2013a and the thermodynamic data were obtained from the NIST REFPROP CO2 data chart [30]. The entropy data of flue gas were obtained from Cengel and Michael data table [31]. Assumptions for this simulation are shown in Table 2. The flowchart of the entire simulation procedure is given in Fig. 4. First, all the input parameters have been specified and then the state points in the T-s diagram have been formulated one by one. 3.1. Energy analysis The energy analysis was done using the first law of thermodynamics, i.e. heat and mass balance. Component-wise energy analysis and mass balance equations at interaction points are given in Tables 3a and 3b. The isentropic efficiencies of three turbomachine units and the recuperator efficiencies were used to calculate state points:

Pump :

gp ¼

Compressor :

h2;is  h1 h2  h1

gc ¼

h4;is  h9 h4  h9

ð1Þ

ð2Þ

S. Banik et al. / Applied Thermal Engineering 107 (2016) 441–452

445

Fig. 4. Flowchart for the simulation of the cycle state points.

Table 3a Component-wise energy balance equations. Component

Equation

1

Pump

2

Compressor

_ p¼m _  ð1  rÞ  ðh2  h1 Þ W _ c ¼m _  r  ðh4  h9 Þ W

3

Turbine

4

Precooler

5

WHRU

6

HTR

7

LTR

8

Contact Heater

LTR :

h3  h2 cp;2  ð1  rÞ  ðT 8  T 2 Þ

ð5Þ

The net power output was given by:

_ net ¼ W _ t W _ pW _c W

_ t¼m _  ðh6  h7 Þ W _  ð1  rÞ  ðh9  h1 Þ Q_ pc ¼ m _  ðh6  h5 Þ Q_ H ¼ m

_  ðh7  h8 Þ ¼ m _  gr  ðh5  h4 Þ Q_ HTR ¼ m _  ðh8  h9 Þ ¼ m _  gr  ð1  rÞ  ðh3  h2 Þ Q_ LTR ¼ m _  h4a  r  m _  h3  ð1  rÞ  m _  h4 Q_ CH ¼ m

ð6Þ

The thermal efficiency or the first law efficiency was defined as the ratio of the power output obtained from the cycle to the heat input (i.e. waste heat recovered). Hence, the first law efficiency of the cycle was:

_ W

gth ¼ _ net QH

ð7Þ

Component

Equation

For a flue gas temperature of 200 °C, an approximate loss of 10– 30% of heat input through fuel occurs [32]. A part of this waste heat can be recovered in the waste heat recovery unit of the cycle. The _ f is mass flow rate of the flue gas, m

Bypass point Contact Heater

_9¼m _1 þm _4 m _3 þm _4 _ 4a ¼ m m

_f ¼ m

Table 3b Mass balance equations.

1 2

eLTR ¼

Q_ H cpf  ðT f ;in  T f ;out Þ

ð8Þ

where cpf was isobaric specific heat.

Turbine :

HTR :

gt ¼

eHTR ¼

h6  h7 h6  h7;is

h5  h4a cp;4a  ðT 7  T 4a Þ

ð3Þ

3.2. Exergy analysis

ð4Þ

Exergy is defined as the maximum theoretical useful work (i.e. work potential) obtained from a system. Exergy, as a parameter, can be utilised to estimate the effectiveness of a cycle with respect

S. Banik et al. / Applied Thermal Engineering 107 (2016) 441–452

to an ideal cycle. Irreversibility or exergy destruction provides the quantity of the wasted work potential. By definition, irreversibility is the difference between the ideal reversible work and the actual work in a cycle [33]. The kinetic and potential energies were neglected. Hence, the exergy rate of a fluid stream at a particular state was defined as:

_  h0  T 0 ðs  s0 Þ E_ ¼ m½h

ð9Þ

The terms T0 and h0 represent the dead state temperature and enthalpy respectively. Hence, the entropy generation rate was:

S_ gen ¼

X

_ out sout  m

X

_ in sin  m

X Q_ T

6

400 4 7

350 5 4a

300

8

3

2

9 10

1

250 0.8

ð10Þ

Hence, according to Gouy-Stodola theorem [34] the rate of irreversibility was:

I_ ¼ T 0 S_ gen

450

Temperature (K)

446

1

1.2

1.4

1.6

1.8

2

2.2

Entropy (KJ/kg-K) Fig. 5. T-s diagram for a transcritical cycle with Q = 2000 K, Pressure ratio = 2.4, mass recompression ratio = 0.4.

ð11Þ

The component-wise exergy balance equations used are given in Table 4. Reddy et al. [35] described the exergetic efficiency as:

Actual thermal efficiency Maximum possible=Reversible thermal efficiency Exergy output ¼ Exergy input

Table 5 State parameters at different points on the transcritical cycle plot at recompression ratio of 0.4 and pressure ratio of 2.4 (P1 = 5000 kPa, P2 = 12,000 kPa).

gII ¼

State points

P (kPa)

T (K)

s (kJ/kg K)

h (kJ/kg)

Hence, the 2nd law efficiency, gII was defined as the total exergy utilised by the cycle to the total exergy of the incoming flue gas stream.

1 2 3 4a 5 4 6 7 8 9 10

5000 12,000 12,000 12,000 12,000 12,000 12,000 5000 5000 5000 5000

287.43 296.09 296.44 307.87 327.32 381.75 443.00 370.08 308.61 301.56 287.43

1.12 1.13 1.14 1.36 1.55 1.88 2.12 2.13 1.85 1.86 1.75

237.87 248.05 250.67 348.75 377.40 495.88 590.22 538.88 450.29 448.72 417.66

gII ¼

Ef ;in  Itot  Ef ;out Ef ;in

ð12Þ

where Ef,in was the exergy of the flue gas inlet stream, Ef,out was the P lost exergy of the flue gas outlet stream and Itot ¼ Icomponenets was the total exergy loss in the system [36].

4. Results and discussions Thermodynamic modelling for the CO2 power cycles as described in Section 3 was used to carry out parametric studies for varying pressure ratio and recompression mass ratio. Variations of both energy and exergy performance of CO2 power cycles for these two parameters are discussed. Comparison of the performance of the trans-critical cycle with corresponding supercritical and regenerative Brayton cycles are also presented. T-s diagram for a specific set of parameters (waste heat = 2000 W, P1 = 5000 kPa, P2 = 12,000 kPa and recompression ratio = 0.4) is shown in Fig. 5 and the corresponding state point data are given in Table 5.

4.1. Model validation A simulation of the thermodynamic T-CO2 power cycle with recompression has been carried out in ASPEN Plus V8.6 to validate the proposed mathematical model. A schematic representation of the study is given in Fig. 6. All the components are identical to the cycle used in the mathematical modelling and CO2 is the working fluid. Identical isentropic efficiencies have also been assigned to the equipment. Work done by turbine, pump and compressor in ASPEN at a specific set of parameters (Q = 2000 kW, P1 = 5000 kPa, P2 = 12,000 kPa, Turbine Inlet Temperature, TIT = 170 °C) has been compared with the values obtained from the mathematical model in Table 6a. Similar comparison has also been made with P1 = 6000, P2 = 12,000 kPa and TIT = 170 °C and shown in Table 6b. The comparison of efficiencies calculated from the ASPEN simulation and MATLAB modelling for various recompression mass

Table 4 Component-wise irreversibility equations. Component

Equation

1 2 3 4

Pump Compressor Turbine Precooler

5

WHRU

6 7 8

HTR LTR Contact Heater

_  ðs2  s1 Þ Ip ¼ T a  ð1  rÞ  m _  ðs4  s9 Þ Ic ¼ T a  r  m _  ðs7  s6 Þ It ¼ T a  m h i _ _  ðs1  s9 Þ  QTcond Ipc ¼ T a  ð1  rÞ  m L   _ f  ðsf ;out  sf ;in Þ þ m _  ðs6  s5 Þ IWHRU ¼ T a  m _  ½fðh8  h7 Þ  T a  ðs8  s7 Þg  fðh5  h4a Þ  T a  ðs5  s4a Þg IHTR ¼ m _  ½fðh9  h8 Þ  T a  ðs9  s8 Þg  ð1  rÞ  fðh3  h2 Þ  T a  ðs3  s2 Þg ILTR ¼ m h i _ _  s4a  m _  r  s3  m _  ð1  rÞ  s4  QT ch ICH ¼ T a  m ch

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S. Banik et al. / Applied Thermal Engineering 107 (2016) 441–452

FLUEOUT COMPR

PUMP

WHRU 2

9

1

5

4

6

CH

LTR

TURBINE

HTR

4A

PC

FLUEIN

3

8 COLDIN

7

HOTOUT

Fig. 6. Schematic representation of the recompression T-CO2 cycle for ASPEN simulation.

Table 6a Energy parameters at different recompression ratios but constant pressure ratio (P1 = 5000 kPa, P2 = 12,000 kPa, TIT = 170 °C). r

Wt (kW) (Aspen)

Wt (kW) (MATLAB)

Wc (kW) (Aspen)

Wc (kW) (MATLAB)

Wp (kW) (Aspen)

Wp (kW) (MATLAB)

Wnet (kW) (Aspen)

Wnet (kW) (MATLAB)

0.3 0.4 0.5 0.6

428.52 499.74 581.05 685.01

455.55 527.24 627.95 771.11

101.97 189.06 312.72 494.06

121.54 207.02 341.91 553.92

56.14 58.63 53.3 50.47

63.26 62.75 62.28 61.18

270.41 252.05 215.03 140.47

270.75 257.47 223.76 156.01

Table 6b Energy parameters at different recompression ratios but constant pressure ratio (P1 = 6000 kPa, P2 = 12,000 kPa, TIT = 170 °C). r

Wt (kW) (Aspen)

Wt (kW) (MATLAB)

Wc (kW) (Aspen)

Wc (kW) (MATLAB)

Wp (kW) (Aspen)

Wp (kW) (MATLAB)

Wnet (kW) (Aspen)

Wnet (kW) (MATLAB)

0.3 0.4 0.5 0.6

416.38 452.48 526.87 543.14

428.321 471.03 517.86 577.94

122.74 171.45 277.8 369.27

114.76 175.94 261.22 391.01

59.8 59.7 55.41 51.93

56.69 54.13 51.34 48.43

233.84 221.33 193.66 121.94

257.171 241.66 205.30 138.50

15

9

6

st

1 law efficiency (%)

12

Modelling, r p=2.4 Simulation, r p=2.4 Modelling, r p=2 Simulation, r p=2

3

ratios is shown in Fig. 7. This figure suggests that the model predicts the value obtained from the simulation within 9.96%, with an average prediction error of 4.12 and 8.78% respectively for both pressure ratios. Variation of efficiency with TIT, using the parameters P1 = 5000 kPa, P2 = 12,000 kPa, r = 0.3 and r = 0.4 in Fig. 8, also shows a maximum absolute error of 12.59%, that corresponds to an average prediction error of 8.93 and 11.1% for both recompression ratios respectively. The source of errors can be attributed to the small differences in the values of property tables used in the ASPEN and mathematical modelling. The ASPEN simulation has been done using BenedictWebb-Rubin-Starling equation of state, while NIST REFPROP uses the modified Benedict-Webb-Rubin equation of state, an Extended Corresponding States (ECS) model, along with the Helmholtz free energy function for pure substances. But, the subcomponent model inaccuracies in calculating the state points and their properties are well within acceptable limits.

0 0.3

0.4

0.5

0.6

Recompression mass ratio Fig. 7. Comparison of first law efficiencies vs recompression mass ratio for cycle modelling and simulation (Q = 2000 kW, P2 = 12,000 kPa, TIT = 170 °C).

4.2. Energy analysis Power outputs as well as power consumption for the T-CO2 power cycle with varying recompression mass ratio are shown in

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S. Banik et al. / Applied Thermal Engineering 107 (2016) 441–452

First law efficiencies varying with recompression mass ratio, for two different precooler pressures are shown in Fig. 10. The Turbine Inlet Pressures (TIP) has been kept constant at 12,000 kPa, and pressure ratios have been changed. The variation of efficiency shows similar trend to the net power output as heat input to the cycle (i.e. waste heat recovered) is assumed constant. Also, for lower pressure ratios, efficiency increases as the net power output increases. A maximum peak is seen at 13.6% at 0.26 mass recompression ratio for rp = 2.4. Similar variations of power and efficiency with pressure ratio for a given recompression mass ratio are shown in Figs. 11 and 12 respectively. With higher pressure ratio both power inputs and output increase. In effect, net power output increases as shown in Fig. 11. First law efficiency variation is also accordingly as shown in Fig. 12. However, according to assumed model, first law efficiency is higher for lower recompression mass ratio. Zhou et al. [5] obtained a maximum efficiency of 8.5 using a R123 based ORC. However, using a trans-critical CO2 with recompression, the maximum estimated efficiency of the present work is 13.6%.

16

st

1 law efficiency (%)

20

12

Simulation, r=0.3 Modeling, r=0.3 Simulation, r=0.4 Modeling, r=0.4

8 160

170

180

190

200

210

220

TIT (Celsius) Fig. 8. Comparison of first law efficiencies vs TIT for cycle modelling and simulation (Q = 2000 kW, P1 = 5000 kPa, P2 = 12,000 kPa).

15

12

1 law efficiency (%)

800

0

9

6

st

Power (kW)

400

3 Wt Wc Wp Wnet

-400

r p=2.4 r p=2

0 0.0

-800 0.0

0.2

0.4

0.6

0.2

0.8

Recompression mass ratio

0.4

0.6

0.8

Recompression mass ratio Fig. 10. Variation of 1st law efficiency with recompression mass ratio (TIP = 12,000 kPa).

Fig. 9. Variation of component power with recompression mass ratio (Q = 2000 kW, TIP = 12,000 kPa, rp = 2.4).

500 400 300 200

Power (kW)

Fig. 9. Power outputs are positive and consumption is negative and is shown accordingly. It is observed from Fig. 9 that power consumption of pump decreases with higher recompression mass ratio, though insignificantly. It is due to lower mass flow rate of liquid CO2 through the pump. Pump power also varies with variation of flow rate of CO2 as well as pressure ratio across the pump. However, the relative variation of pump power is insignificant with respect to both compressor and turbine powers as shown in the figure. Consumption of power in compressor increases with recompression mass ratio, almost linearly up to 0.4. Then rate of increase is higher. Similar trend is observed for turbine power output. For higher recompression mass ratio, temperature after contact heater increases. As a result, temperature after HTR (i.e. T5) increases. For assumed constant heat input in waste heat recovery unit, mass flow rate increases. As CO2 was modelled as real gas, the enthalpy change for CO2 was non-linear with corresponding temperature change of it. This effect is reflected in rapid increase of power input/output in compressor/turbine beyond recompression mass ratio of 0.4. In effect, net power output decreases with higher recompression mass ratio.

100 0 -100 -200

Wt Wc Wp Wnet

-300 -400 1.9

2.0

2.1

2.2

2.3

2.4

Pressure ratio Fig. 11. Variation of component power with pressure ratio (Q = 2000 kW, r = 0.4, TIP = 12,000, transcritical).

S. Banik et al. / Applied Thermal Engineering 107 (2016) 441–452

13

11

10

st

1 law efficiency (%)

12

r=0.3 r=0.4 r=0.5

9

8 1.9

2.0

2.1

2.2

2.3

2.4

Pressure ratio Fig. 12. Variation of 1st law efficiency with pressure ratio (TIP = 12,000 kPa).

17

15

st

1 law efficiency (%)

16

14 r p=2.4 r p=2

13 0.0

0.2

0.4

0.6

0.8

Recompression mass ratio Fig. 13. Variation of 1st law efficiency with recompression mass ratio (constant precooler inlet, TIP = 12,000 kPa).

Economic impact can be grossly assessed by estimating the physical size of a component as well as unit price of the material. In heat exchange process, these effects may be combined in a parameter ‘‘UA” – product of overall heat transfer coefficient and total surface area for the heat exchange process. It is interesting to note that for a constant precooler inlet temperature (constant pinch), the total recuperator ‘‘UA” increases and efficiency increases with recompression mass ratio as shown in Fig. 13. It is a reverse trend than corresponding variation for constant pressure ratio as shown in Fig. 10. Thus, for increasing overall heat transfer infrastructure (i.e. constant ‘‘UA”) first law efficiency of the cycle increases with higher recompression mass ratio. For similar conditions as before, the highest efficiency is 16.3% at an rp = 2.4. Hence, for higher efficiencies, it is beneficial to have a higher ‘‘UA” value to facilitate better heat transfer. 4.3. Exergy analysis Performance of a power generation unit is not only estimated by the first law efficiency but also by its possible potential for

449

improvement, assessed by exergy analysis. Irreversibility in components of the plant for the assumed model is shown for different recompression mass ratios in Fig. 14. It is observed that maximum irreversibility occurs in the waste heat recovery unit. As the total mass flow of CO2 exchanges heat across a finite temperature difference, the irreversibility is most prominent for this component of the plant. However, with higher recompression mass ratio, this irreversibility decreases as preheating of CO2 in contact heater decreases the temperature difference during heat transfer in waste heat recovery unit. Next to it, irreversibility occurs in contact heater. This irreversibility is due to mixing of two streams of CO2 at different temperatures. Irreversibilities in HTR and turbine come next respectively. Irreversibilities in other components are not that significant as shown in Fig. 14. Combined effect of irreversibilities in all components is shown in Fig. 15. Total irreversibility is the addition of irreversibilities in different components of the plant. For a recompression S-CO2 cycle, Bryant et al. [37] reported that with recompression mass ratios above 0.35 the efficiency of the cycle decreases rapidly. Kim et al. [25] recommended a recompression mass ratio of 0.4 for his LH T-CO2 power cycle. For the proposed cycle, the total irreversibility optimises for minimum total irreversibility at a recompression mass ratio of 0.48 as shown in Fig. 15. At this point there is a significant balance in the decrease in irreversibility in WHRU to that of the increase in HTR and precooler. Irreversibilities in different components of the plant with varying turbine pressure ratios for a given recompression mass ratio (i.e. 0.4) is shown in Fig. 16 and the combined effect is shown in Fig. 17. Relative contributions for irreversibilities of different components are obviously similar to the previous case. However, total irreversibility decreases with higher pressure ratio due to the decreasing effects of precooler and HTR irreversibilities. With higher pressure ratio there is a decrease in the irreversibilities of both precooler and the HTR. The increase in the irreversibility of WHRU is not significant even though it reaches the 500 kW mark at rp = 2.3. Second law efficiencies with varying recompression mass ratio (Fig. 18) and pressure ratio (Fig. 19) complies with the total irreversibility plots. The minimum total irreversibility point at r = 0.48, also produce a high second law efficiency of 26.7%. Higher second law efficiencies with higher pressure ratio can also be conformed from the total irreversibility plot. Higher values of exergetic efficiencies above 26% has been obtained at rp = 2.3, which also suggests a increase over that of r = 0.3. But the closeness of the curves at r = 0.4 and r = 0.5 suggests a possible point of optimum between them. In view of irreversibility and decreasing thermal efficiency the recommended recompression mass ratio is within the range of 0.4–0.5. 4.4. Performance comparison of CO2-based transcritical cycle vs supercritical and regenerative Brayton cycles Results using developed model for transcritical cycle is explained in Sections 4.1 and 4.2. Results are also obtained for supercritical and regenerative Brayton cycles with same turbine inlet pressure and temperature. Being supercritical, turbine inlet pressure is different for these two cycles from the transcritical one, in order to keep the turbine pressure ratio constant for all the three cycles. Also, recompression is not valid for regenerative Brayton, though similar recompression ratio is used for supercritical and transcritical cycles. Thus all operating parameters of these three compared cycles are not exactly same, but similar. The basic idea of comparing these three cycles is to explore best option out of these three for an available waste heat type. Efficiency variation with pressure ratio is shown in Fig. 20. The recompression mass ratio is 0.4 for both the recompression cycles

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S. Banik et al. / Applied Thermal Engineering 107 (2016) 441–452

600.00

548.06 502.29 450.86

400.00

Ip Ic Iwhru

300.00

It

0.20

0.40

112.64

ILTR Ipc ICH

2.21 13.52

60.85 71.23

51.40 7.86

0.48 5.58

45.04 59.80

23.24

8.73

117.87

0.09 4.00

0.00

9.46 9.09

100.00

82.92

IHTR

200.00 36.62 58.45

Irreversibility (kW)

500.00

0.60

Recompression mass ratio Fig. 14. Variation of component irreversibility with recompression mass ratio (TIP = 12,000 KPa, rp = 2.4, Q = 2000 kW).

and the amount of available waste heat (Q = 2000 kW) is constant for all the three cycles. T-CO2 recompression cycle offers better efficiency than the S-CO2 recompression cycle. However its efficiency is lower than that of the regenerative Brayton cycle. Bryant et al. [37] observed that recompression cycles always require more recuperator surface area (larger ‘‘UA”) in order to achieve the benefits over the simple Brayton cycle. He showed that up to a certain small initial UA value, the efficiencies of both cycles remained same. Then the performance of the recompression cycle excelled over the simple supercritical Brayton ones for larger recuperator UA values. The total recuperator area is kept identical in this study for all three cycles. Based on assumptions made, the S-CO2 cycle with recompression is found to have lowest efficiency out of three cycles. The second law efficiency of the trans-critical recompression cycle is the best among the three. From Fig. 21, second law efficiency of transcritical cycle reaches a maximum at 27%, whereas the same of supercritical recompression and regenerative Brayton CO2 cycles come next to it respectively.

900

800

700

600 0.2

0.4

0.6

0.8

Recompression mass ratio Fig. 15. Variation of total irreversibility with recompression mass (TIP = 12,000 kPa, rp = 2.4).

ratio

600 466.9

483.13

496.31 Ip Ic

400

Iwhru

300

It IHTR

0

1.90

43.06 77.92 3.46 37.34 81.38

4.82 23.47

100

41.28 87.1 8.33 68.77 79.42

200 1.78 23.68

Irreversibility (kW)

500

2.10

44.76 65.89 1.14 14.37 82.82

0.0

7.49 23.4

Total irreversibility (kW)

1000

ILTR Ipc Ich

2.30

Pressure ratio Fig. 16. Variation of component irreversibility with pressure ratio (Q = 2000 kW, r = 0.4, TIP = 12,000, transcritical cycle).

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14

800

12

1 law efficiency (%)

760

740

10

st

Total irreversibility (kW)

780

8 720

r=0.3 r=0.4 r=0.5

Reg. Braton T-CO2 S-CO2

700

6 1.9

2.0

2.1

2.2

2.3

1.8

2.4

1.9

Pressure ratio

2.0

2.1

2.2

2.3

Pressure ratio

Fig. 17. Variation of total irreversibility with pressure ratio (TIP = 12,000 kPa).

Fig. 20. Variation of cycle efficiencies with pressure ratio for the three cycles (Q = 2000 kW, r = 0.4).

28

28

26 20

2 law efficiency (%)

16

24

22

nd

nd

2 law efficiency (%)

24

r p=2.4

12

20

r p=2

T-CO 2

0.0

0.2

0.4

0.6

0.8

S-CO 2

18

Reg. Brayton

Recompression mass ratio Fig. 18. Variation of second law efficiency with recompression mass ratio (TIP = 12,000 kPa).

1.9

2.0

2.1

2.2

2.3

Pressure ratio Fig. 21. Variation of second law efficiencies with pressure ratios for the three cycles (Q = 2000 kW, r = 0.4).

27

5. Conclusions

26

25

24

nd

2 law efficiency (%)

1.8

23

r=0.3 r=0.4 r=0.5

22 1.9

2.0

2.1

2.2

2.3

2.4

Pressure ratio Fig. 19. Variation of second law efficiency with pressure ratio (TIP = 12,000 KPa).

Increasing energy efficiency is a way to future energy sustainability. Significant part of energy input through fuel is lost as waste heat in industrial processes. Recovery of waste heat may be a possible option for increasing energy efficiency. Lower the temperature, more difficult it is to recover the waste heat. Generation of power using CO2 cycle is a prospective option for recovery and utilisation of low temperature industrial waste heat. Performance of a T-CO2 power cycle has been explored using a developed thermodynamic model. Effects of pressure ratio and recompression on the performance are specifically explored. A comparison of the performance of this T-CO2 power cycle with corresponding supercritical and regenerative Brayton cycles are also discussed.
The mathematical model described in this study predicts the calculated efficiencies from an ASPEN simulation, using identical parameters, within 12.59%.

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First law efficiency of the cycle decreases with increasing recompression mass ratio, assuming no constraint on the size of recuperators. Though, the same increases for higher recompression mass ratio, if the physical sizes of recuperators are kept constant. Maximum thermal efficiency of the cycle is found to be 13.6% at 0.26 mass recompression ratio for rp = 2.4.
If the precooler inlet temperature is kept constant, the overall ‘‘UA” increases and the efficiency increase up to 16.3% for the same conditions. But it requires higher recuperator surface area and hence increased cost.
An optimum value of recompression mass ratio is obtained as 0.48 for which total irreversibility of the cycle is a minimum (27%). WHRU comprises the maximum percentage in total irreversibility, with values ranging from 550 to 450 kW at 0.2 to 0.6 recompression mass ratio. Precooler and HTR contributes to the maximum change in total irreversibilities.
Thermal efficiency of the transcritical cycle is found to be in between regenerative Brayton and supercritical cycle for the same pressure ratio. However, the rate of increase of efficiency with pressure ratio is a maximum for T-CO2 cycle among these three cycles. However, the second law efficiency of T-CO2 cycle is higher than other two cycles.

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